Question: In how many ways can 9 people sit around a round table?  (Two seatings are considered the same if one is a rotation of the other.)
Solution: There are $9!$ ways to arrange 9 people in a line, however there are 9 identical rotations for each arrangement, so we divide by 9 to get $\dfrac{9!}{9} = 8! = \boxed{40,\!320}$.